The table shows the candle's height over time as it burns. We can calculate the rate at which the candle is burning by examining the decrease in height over time and using this to determine the correct statement.

Step 1: Calculate the rate of change

We need to find the rate at which the candle burns. To do this, we can subtract consecutive height values and divide by the change in time.

1. From 0 to 0.25 hours: $\frac{25 - 24.375}{0.25 - 0} = \frac{0.625}{0.25} = 2.5 \, \text{cm/hour}$

2. From 0.25 to 0.5 hours: $\frac{24.375 - 23.75}{0.5 - 0.25} = \frac{0.625}{0.25} = 2.5 \, \text{cm/hour}$

3. From 0.5 to 0.75 hours: $\frac{23.75 - 23.125}{0.75 - 0.5} = \frac{0.625}{0.25} = 2.5 \, \text{cm/hour}$

4. From 0.75 to 1 hour: $\frac{23.125 - 22.5}{1 - 0.75} = \frac{0.625}{0.25} = 2.5 \, \text{cm/hour}$

So, the candle burns at a constant rate of 2.5 cm per hour.

Step 2: Identify the initial height

From the table, the initial height at time $t = 0$ is 25 cm.

Step 3: Choose the correct statement

The candle starts at a height of 25 cm and burns at a rate of 2.5 cm per hour.

Thus, the correct statement is:

• The candle starts at a height of 25 centimeters and burns at a rate of 2.5 centimeters per hour.

Would you like further details on this, or have any additional questions? Here are 5 related questions:

1. How would the equation of the candle's height as a function of time look?
2. How long will it take for the candle to completely burn out if it starts at 25 cm?
3. If the rate changed halfway, how would you determine the new burning rate?
4. What other factors could affect the burning rate of the candle?
5. How can we verify that the rate is consistent over time?

Tip:

To calculate the rate of change in a function, always divide the difference in the dependent variable (height) by the difference in the independent variable (time).